JEE Mains · Maths · STD 11 - 13. statistics
If the mean and the variance of the data
| Class | 4-8 | 8-12 | 12-16 | 16-20 |
| Frequency | 3 | \(\lambda\) | 4 | 7 |
- A 18
- B 21
- C 20
- D 19
Answer & Solution
Correct Answer
(D) 19
Step-by-step Solution
Detailed explanation
\(\mu=\frac{\sum f_i x_i}{\sum f_i}=\frac{18+10 \lambda+56+126}{14+\lambda}\) \(=\frac{200+10 \lambda}{\lambda+14}=10+\left(\frac{60}{\lambda+14}\right)\) \(\lambda+14\) is multiply of \(60 \Rightarrow \lambda=1\) or 6 or 16. \(\sigma^2=\frac{\sum x_1^2}{\lambda+14}-(\mu)^2\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3 \quad\) and \(\quad|\vec{a} \times \vec{b}|^{2}=75\).Then \(|\vec{a}|^{2}\) is equal to \(.......\)JEE Mains 2022 Hard
- Let \(P\) be the point \((10,-2,-1)\) and \(Q\) be the foot of the perpendicular drawn from the point \(\mathrm{R}(1,7,6)\) on the line passing through the points \((2,-5,11)\) and \((-6,7,-5)\). Then the length of the line segment \(\mathrm{PQ}\) is equal to ..........JEE Mains 2024 Medium
- If \(\left({ }^{40} C _{0}\right)+\left({ }^{41} C _{1}\right)+\left({ }^{42} C _{2}\right)+\ldots+\left({ }^{\infty} C _{20}\right)=\frac{ m }{ n }{ }^{60} C _{20}, m\) and \(n\) are coprime, then \(m+n\) is equal toJEE Mains 2022 Hard
- The angle of elevation of the top \(P\) of a tower from the feet of one person standing due South of the tower is \(45^{\circ}\) and from the feet of another person standing due west of the tower is \(30^{\circ}\). If the height of the tower is \(5\) meters, then the distance (in meters) between the two persons is equal to \(..........\).JEE Mains 2023 Medium
- Consider the lines \(\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5\), \(\lambda\) being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of \(L\) from the point \((3,6)\) is \(d\), then the value of \(d^2\) isJEE Mains 2025 Easy
- Five digit numbers are formed using the digits \(1,2 , 3,5,7\) with repetitions and are written in descending order with serial numbers. For example, the number \(77777\) has serial number \(1\). Then the serial number of \(35337\) is \(.........\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- If the system of equations \(x+y+a z=b\) \(2 x+5 y+2 z=6\) \(x+2 y+3 z=3\) has infinitely many solutions, then \(2 a+3 b\) is equal to \(...........\).JEE Mains 2023 Medium
- Two vertices of a triangle \(\mathrm{ABC}\) are \(\mathrm{A}(3,-1)\) and \(\mathrm{B}(-2,3)\), and its orthocentre is \(\mathrm{P}(1,1)\). If the coordinates of the point \(\mathrm{C}\) are \((\alpha, \beta)\) and the centre of the circle circumscribing the triangle \(\mathrm{PAB}\) is \((h, k)\), then the value of \((\alpha+\beta)+2(h+k)\) equals :JEE Mains 2024 Hard
- Let \(A = \left\{ {\left( {x,y} \right):{y^2} \le 4x,y - 2x \ge - 4} \right\}\) .The area of the region \(A\) isJEE Mains 2014 Hard
- Let \(f :[-3,1] \rightarrow R\) be given as \(f(x)=\left\{\begin{array}{ll} \min \left\{(x+6), x^{2}\right\}, & -3 \leq x \leq 0 \\ \max \left\{\sqrt{x}, x^{2}\right\}, & 0 \leq x \leq 1 \end{array}\right.\) If the area bounded by \(y = f ( x )\) and \(x\) -axis is \(A,\) then the value of \(6 A\) is equal to ....... .JEE Mains 2021 Hard
- If the volume of a spherical ball is increasing at the rate of \(4 \pi \, cc/sec\), then the rate of increase of its radius (in \(cm/sec\)), when the volume is \(288 \pi \, cc\)JEE Mains 2014 Hard
- The distance, from the origin, of the normal to the curve, \(x = 2\,cos\,t + 2t\,sin\,t,\,\,y = 2\,sin\,t -2t\, cos\,t\) at \(t= \frac {\pi }{4},\) isJEE Mains 2015 Hard